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Alexxx [7]
3 years ago
15

(-2,1); perpendicular to y= - 2/5x -4 Help explain step by step?

Mathematics
1 answer:
Fittoniya [83]3 years ago
8 0

Answer:

  y = (5/2)x + 6

Step-by-step explanation:

The given line has a slope (coefficient of x) of -2/5. The perpendicular line will have a slope that is the negative reciprocal of this:

  -1/(-2/5) = 5/2

Since you are given a point you want the line to go through, the point-slope form of the equation of the line is useful. That form for slope m and point (h, k) is ...

  y = m(x -h) +k

For your slope m=5/2 and point (h, k) = (-2, 1), the equation of the line is ...

  y = 5/2(x +2) +1

  y = 5/2x +6 . . . . . eliminate parentheses

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Let g be the function given by g(x)=limh→0sin(x h)−sinxh. What is the instantaneous rate of change of g with respect to x at x=π
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The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>.

<h3>How to determine the instantaneous rate of change of a given function</h3>

The <em>instantaneous</em> rate of change at a given value of x can be found by concept of derivative, which is described below:

g(x) =  \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}

Where h is the <em>difference</em> rate.

In this question we must find an expression for the <em>instantaneous</em> rate of change of g if f(x) = \sin x and evaluate the resulting expression for x = \frac{\pi}{3}. Then, we have the following procedure below:

g(x) =  \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h}

g(x) =  \lim_{h \to 0} \frac{\sin x\cdot \cos h +\sin h\cdot \cos x -\sin x}{h}

g(x) =  \lim_{h \to 0} \frac{\sin h}{h}\cdot  \lim_{h \to 0} \cos x

g(x) = \cos x

Now we evaluate g(x) for x = \frac{\pi}{3}:

g\left(\frac{\pi}{3} \right) = \cos \frac{\pi}{3} = \frac{1}{2}

The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>. \blacksquare

To learn more on rates of change, we kindly invite to check this verified question: brainly.com/question/11606037

4 0
2 years ago
Can someone help me please
Taya2010 [7]

Answer:

n = -1

Step-by-step explanation:

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N^2 +2n +1 = 0       (subtract 3n from both sides)

(n+1)(n+1) = 0   (factor

n+1 =0; n= -1

n+1 = 0  ; n=-1

4 0
3 years ago
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